The fundamental element of a quantum computer is the quantum bit—also known as the “qubit”. As opposed to a classical bit, representing zero and one, a qubit is also able to represent a quantum superposition of the two states. Hence, the states can be formalized within the laws of quantum physics, with a probability. Accordingly, the states can be manipulated and observed within the laws of quantum physics.
A number of physical objects have been suggested as potential implementations of qubits. However, solid-state circuits, and superconducting circuits in particular, are of great interest as they offer scalability—a possibility of making circuits with a larger number of interacting qubits. Superconducting qubits are typically based on Josephson junctions (JJ). A Josephson junction is basically two superconductors coupled by a weak link. The weak link can for example be a thin insulating barrier, a short section of non-superconducting metal, or a physical constriction that weakens the superconductivity at the point of contact.
A Josephson junction can be fabricated by means an insulating Al2O3 tunnel barrier, i.e. the weak link, between superconducting electrodes. For such superconductor-insulator-superconductor (SIS) Josephson junctions, the maximum allowed supercurrent, the critical current, IC, and the Josephson coupling energy, EJ=ℏIC/2e, where e is the electron charge, are determined by the JJ area and insulator thickness and fixed by sample fabrication.
One of the first qubits to be realized was a charge qubit: a single cooper pair box. The single cooper pair box consists of a small island, connected to a superconducting reservoir through a JJ on one side and biased by a gate capacitance Cg and a gate voltage Vg on the other side. When the junction is in its superconducting state, Cooper pairs can tunnel to and from the island. The potential of the island can be controlled through the gate voltage. In addition to the Josephson coupling energy, the single cooper pair box can also be characterized by the Coulomb energy of the Cooper pair, i.e. the charging energy, given as EC=e2/2CT, where CT represents the total capacitance between the island and its circuit, i.e. CT=Cg+CJ, where CJ is the capacitance of the JJ.
Superconducting qubits having a tunable critical current and based on Josephson junctions are preferred in the field of quantum computing, and have been realized using a so-called superconducting quantum interference device (SQUID), which allow Ej to be tuned by means of an external magnetic field.
The SQUID is based on an add-on to the single cooper box, in that it for example may have a JJ added in parallel to the JJ of the single cooper pair box, thereby forming a loop, through which a magnetic field can be applied. In this configuration, the SQUID is a so-called DC-SQUID. The typical charge qubit, being the simple single cooper pair box, is thus obsolete, at least because it is non-tunable.
Several problems are however related to a tuneable qubit, in particular to an external magnetic field as applied in order to tune the qubit. First of all, an external magnetic field could decrease the ratio of the Josephson energy and the charging energy, thereby introducing sensitivity to charge noise. Secondly, magnetic flux could be entrapped in the system. Thirdly, it could be inconvenient to place a magnet in close vicinity of one or more qubits. Finally, it could be complex to manage the magnetic field for interacting qubits.